What is the limit as x approaches 0 of x/(x^3+5x) ?

The limit as x approaches 0 of x/(x^3+5x) is 1/5

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limit as x approaches 0 of x/(x^3+5x)

x \to 0 lim (\frac{x}{x ^{3} + 5 x})

\frac{1}{5}

Decimal

0.2

Solution steps

x \to 0 lim (\frac{x}{x ^{3} + 5 x})

Simplify

\frac{x}{x ^{3} + 5 x} : \frac{1}{x ^{2} + 5}

= x \to 0 lim (\frac{1}{x ^{2} + 5})

Plug in the value

x = 0

= \frac{1}{0 ^{2} + 5}

Simplify

= \frac{1}{5}

x \to 1 - lim (- \frac{1}{x ^{2} + 6 x - 7})

x \to 0 lim (ln (\frac{x ^{2}}{2}))

θ \to + 0 lim (\frac{sin ( 30 )}{θ})

x \to \infty lim (\frac{1}{x} \cdot 0)

x \to 0 lim (x (\frac{2}{x}))

What is the limit as x approaches 0 of x/(x^3+5x) ?
The limit as x approaches 0 of x/(x^3+5x) is 1/5